Time and Date Stamps (logged): 12:49:21 05-21-2012
°±Ÿ³¸Ÿ±°¯´Ÿ±°Ÿ±¯°±
Precalculus II
University Physics (Phy 231, Phy 241) Test 2
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Test should be printed using Internet Explorer. If
printed from different browser check to be sure test items have not been cut off. If
items are cut off then print in Landscape Mode (choose File, Print, click on Properties
and check the box next to Landscape, etc.).
Name and Signature of Student
_____________________________
Signed by Attendant, with Current Date and Time:
______________________
If picture ID has been matched with student and name as
given above, Attendant please sign here: _________
Instructions:
- Test is to be taken without reference to text or
outside notes.
- Graphing Calculator is allowed, as is blank paper or
testing center paper.
- No time limit but test is to be taken in one
sitting.
- Please place completed test in Dave Smith's folder,
OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va.,
24212-0828 OR email copy of document to dsmith@vhcc.edu,
OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..
Directions for Student:
- Completely document your work.
- Numerical answers should be correct to 3 significant
figures. You may round off given numerical information to a precision consistent
with this standard.
- Undocumented and unjustified answers may be counted
wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or
yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get
partial credit. So show your work and explain your reasoning.
- Due to a scanner malfunction and other errors some
test items may be hard to read, incomplete or even illegible. If this is judged by
the instructor to be the case you will not be penalized for these items, but if you
complete them and if they help your grade they will be counted. Therefore it is to
your advantage to attempt to complete them, if necessary sensibly filling in any
questionable parts.
- Please write on one side of paper only, and staple
test pages together.
Test Problems:
. . . . .
. . . .
. . . .
. . .
.
.
.
.
.
.
.
.
.
.
Problem Number 1
Given that the gravitational potential energy of a mass m at distance r from the
center of a planet of mass M is PE(r) = G M m / r, find the derivative dPE / dr.
- What is the gravitational force on mass m at distance r from the center of the
planet?
- How do your two results compare and why?
.
.
.
.
.
.
.
.
.
.
Problem Number 2
A uniform rod of mass 1.7 kg
and length 60 cm is constrained to rotate on an axis about its center. An unknown
uniform torque is applied to the rod as it rotates through .22 radians from rest, which
requires .8 seconds. The applied torque is then removed and, coasting only under the
influence of friction, the rod comes to rest after rotating through 2.9 radians, which
requires 6 seconds.
- Determine the angular acceleration of the moving rod before and after the torque is
applied.
- Determine the net torque for each phase of the motion.
- What is the applied torque?
- How much work is done by the net torque, by the applied torque and by friction during
the first phase of motion?
.
.
.
.
.
.
.
.
.
.
Problem Number 3
A cart of mass 1 Kg is temporarily held stationary
on an incline at 7 degrees to horizontal. A mass of .22 Kg is attached to the cart
by a string over a pulley located at the top of the incline; the mass hangs freely from
the string. When the cart is released from rest, it accelerates through a distance
of 1.5 meters. Assuming no friction or other dissipative forces:
- How much work does gravity do on the cart?
- Using the definition of KE, determine the velocity
attained by the cart.
.
.
.
.
.
.
.
.
.
.
Problem Number 4
If a mass of 4 kg moving at 5 m/s collides with a mass of 7 kg moving at -5
m/s, and the second mass has velocity -2.142857 m/s after collision, then what is the velocity of
the first after collision? Is this collision possible for the system consisting of
the two masses without the conversion of some internal source of potential energy?
.
.
.
.
.
.
.
.
.
.
Problem Number 5
When masses of 55, 110 and 165 grams are hung from a certain rubber band its
respective lengths are observed to be 41, 47 and 53 cm. What are the x and y components of
the tension of a rubber band of length 41.7 cm if the x component of its length if 9.944455 cm?
What force directed at 146 degrees, when added to this force, will result
in a vertical force?
.
.
.
.
.
.
.
.
.
.
Problem Number 6
A uniform sphere is growing in such a way that its radius increases by .3 cm
every minute. The mass density of the sphere is 9 grams per cm^3. If I(r) is
the moment of inertia of the disk when its radius is r, then what are dI / dr and dI
/ dt at the instant the radius is 55 cm?
.
.
.
.
.
.
.
.
.
.
Problem Number 7
What would be the orbital KE of a satellite of mass 760 kg in circular orbit
about a planet of mass 38 * 10^24 kg, orbiting at a distance of 40900 km from the center of
the planet?
By how much would orbital PE change as the satellite moved from this orbit to a
circular orbit of radius 44990 km?
G = 6.67 * 10^-11 N m^2 / kg^2
.
.
.
.
.
.
.
.
.
.
Problem Number 8
At what rate would a Ferris wheel with a radius of 22 meters have to be rotating
in order for a person to feel weightless at the top of the ride?